def extract_backbone(flavor_network, alpha):
"""
makes a new graph with only the edges with weights that exceed the threshold for statistical significance
:param ing_comp_graph: full flavor ingredient network
:return: the pruned SGraph
"""
def degree_count_fn(src, edge, dst):
"""
increments the degree of the nodes on this edge
:param src:
:param edge:
:param dst:
:return:
"""
src['deg'] += 1
dst['deg'] += 1
return src, edge, dst
def compute_node_moments(node_k):
mean = 2 * node_k / (node_k + 1)
sigma = sqrt(node_k**2 * ((20 + 4 * node_k) /
((node_k + 1) * (node_k + 2) *
(node_k + 3)) - 4 / (node_k + 1)**2))
return mean, sigma
def test_for_significance(edge, weights_lookup, alpha):
y_obs = edge['weight']
node1_k = weights_lookup[edge['__dst_id']]
node2_k = weights_lookup[edge['__src_id']]
m1, sig1 = compute_node_moments(float(node1_k))
m2, sig2 = compute_node_moments(float(node2_k))
return y_obs >= abs(m1 + alpha * sig1) or y_obs >= abs(m2 +
alpha * sig2)
flav_net_w_deg = SGraph()
edge_list = flavor_network.get_edges()
new_node_list = flavor_network.vertices.fillna('deg', 0)
flav_net_w_deg = flav_net_w_deg.add_vertices(new_node_list).add_edges(
edge_list)
flav_net_w_deg = flav_net_w_deg.triple_apply(degree_count_fn,
mutated_fields=['deg'])
weights_dict = flav_net_w_deg.vertices.to_dataframe().set_index(
'__id').to_dict()['deg']
significant_edges = []
for edge in flav_net_w_deg.get_edges():
if test_for_significance(edge, weights_dict, alpha):
significant_edges.append(
flav_net_w_deg.get_edges(src_ids=edge['__src_id'],
dst_ids=edge['__dst_id'],
format='list')[0])
pruned_network = SGraph().add_vertices(new_node_list)
pruned_network = pruned_network.add_edges(significant_edges)
return pruned_network
def extract_backbone(flavor_network, alpha):
"""
makes a new graph with only the edges with weights that exceed the threshold for statistical significance
:param ing_comp_graph: full flavor ingredient network
:return: the pruned SGraph
"""
def degree_count_fn(src, edge, dst):
"""
increments the degree of the nodes on this edge
:param src:
:param edge:
:param dst:
:return:
"""
src['deg'] += 1
dst['deg'] += 1
return src, edge, dst
def compute_node_moments(node_k):
mean = 2*node_k/(node_k+1)
sigma = sqrt(node_k**2*((20 + 4*node_k)/((node_k + 1)*(node_k + 2)*(node_k + 3)) - 4/(node_k + 1)**2))
return mean, sigma
def test_for_significance(edge, weights_lookup, alpha):
y_obs = edge['weight']
node1_k = weights_lookup[edge['__dst_id']]
node2_k = weights_lookup[edge['__src_id']]
m1, sig1 = compute_node_moments(float(node1_k))
m2, sig2 = compute_node_moments(float(node2_k))
return y_obs >= abs(m1 + alpha*sig1) or y_obs >= abs(m2 + alpha*sig2)
flav_net_w_deg = SGraph()
edge_list = flavor_network.get_edges()
new_node_list = flavor_network.vertices.fillna('deg', 0)
flav_net_w_deg = flav_net_w_deg.add_vertices(new_node_list).add_edges(edge_list)
flav_net_w_deg = flav_net_w_deg.triple_apply(degree_count_fn, mutated_fields=['deg'])
weights_dict = flav_net_w_deg.vertices.to_dataframe().set_index('__id').to_dict()['deg']
significant_edges = []
for edge in flav_net_w_deg.get_edges():
if test_for_significance(edge, weights_dict, alpha):
significant_edges.append(flav_net_w_deg.get_edges(src_ids=edge['__src_id'],
dst_ids=edge['__dst_id'], format='list')[0])
pruned_network = SGraph().add_vertices(new_node_list)
pruned_network = pruned_network.add_edges(significant_edges)
return pruned_network
